As we mentioned above, there are several model structures on
\({K}/B\) . The model structure described in Theorem REF 
above is the most convenient for us, as it is the natural generalization
of the Strøm model structure to parametrized spaces. In [1]}, [2]} a
different model structure on \({K}/B\)  was introduced (following [3]}
we denote this model structure by \(({K}/B)_{ij}\) ) which has the property
that it models homotopy sheaves on \(B\) .
More precisely, in [2]} (see also [3]}) it is proven that there is a
canonical adjunction
\(|-|_B\colon \infty \, \mathrm {Sh}(B)\leftrightarrows ({K}/B)_{ij}\colon \mathrm {Sing}_B\) 
